We show that three different morphologies exist near the two-phase boundary of ternary systems containing a hydrotropic cosolvent. Based on synchrotron small- and wide-angle X-ray scattering combined with molecular dynamics, we rationalize the specific scattering signature of direct, bicontinuous, and reverse mesoscale solubilization. Surprisingly, these mesostructures are resilient toward strong acids, which are required in industrial applications. However, on a macroscopic scale, the phase boundary shifts in salting-in and salting-out in the direct and respectively reverse regime, leading to a crossing of the binodals.